Quick calculus : a self-teaching guide / Daniel Kleppner, Norman Ramsey and Peter Dourmashkin

Includes index.

Preface iii -- Chapter One Starting Out 1 -- 1.1 A Few Preliminaries 1 -- 1.2 Functions 2 -- 1.3 Graphs 5 -- 1.4 Linear and Quadratic Functions 11 -- 1.5 Angles and Their Measurements 19 -- 1.6 Trigonometry 28 -- 1.7 Exponentials and Logarithms 42 -- Summary of Chapter 1 51 -- Chapter Two Differential Calculus 57 -- 2.1 The Limit of a Function 57 -- 2.2 Velocity 71 -- 2.3 Derivatives 83 -- 2.4 Graphs of Functions and Their Derivatives 87 -- 2.5 Differentiation 97 -- 2.6 Some Rules for Differentiation 103 -- 2.7 Differentiating Trigonometric Functions 114 -- 2.8 Differentiating Logarithms and Exponentials 121 -- 2.9 Higher-Order Derivatives 130 -- 2.10 Maxima and Minima 134 -- 2.11 Differentials 143 -- 2.12 A Short Review and Some Problems 147 -- Conclusion to Chapter 2 164 -- Summary of Chapter 2 165 -- Chapter Three Integral Calculus 169 -- 3.1 Antiderivative, Integration, and the Indefinite Integral 170 -- 3.2 Some Techniques of Integration 174 -- 3.3 Area Under a Curve and the Definite Integral 182 -- 3.4 Some Applications of Integration 201 -- 3.5 Multiple Integrals 211 -- Conclusion to Chapter 3 219 -- Summary of Chapter 3 219 -- Chapter Four Advanced Topics: Taylor Series, Numerical Integration, and Differential Equations 223 -- 4.1 Taylor Series 223 -- 4.2 Numerical Integration 232 -- 4.3 Differential Equations 235 -- 4.4 Additional Problems for Chapter 4 244 -- Summary of Chapter 4 248 -- Conclusion (frame 449) 250 -- Appendix A Derivations 251 -- A.1 Trigonometric Functions of Sums of Angles 251 -- A.2 Some Theorems on Limits 252 -- A.3 Exponential Function 254 -- A.4 Proof That dy/dx = 1/dxΓêòdy 255 -- A.5 Differentiating Xn 256 -- A.6 Differentiating Trigonometric Functions 258 -- A.7 Differentiating the Product of Two Functions 258 -- A.8 Chain Rule for Differentiating 259 -- A.9 Differentiating Ln X 259 -- A.10 Differentials When Both Variables Depend on a Third Variable 260 -- A.11 Proof That if Two Functions Have the Same Derivative They Differ Only by a Constant 261 -- A.12 Limits Involving Trigonometric Functions 261 -- Appendix B Additional Topics in Differential Calculus 263 -- B.1 Implicit Differentiation 263 -- B.2 Differentiating the Inverse Trigonometric Functions 264 -- B.3 Partial Derivatives 267 -- B.4 Radial Acceleration in Circular Motion 269 -- B.5 Resources for Further Study 270 -- Frame Problems Answers -- 273 Answers to Selected Problems from the Text -- 273 Review Problems -- 277 Chapter 1 277 -- Chapter 2 278 -- Chapter 3 282 -- Tables 287 -- Table 1: Derivatives 287 -- Table 2: Integrals 288 -- Indexes 291 Index 291 -- Index of Symbols 295.

In Quick Calculus: A Self-Teaching Guide, 3rd Edition, a team of expert MIT educators delivers a hands-on and practical handbook to essential calculus concepts and terms. The author explores calculus techniques and applications, showing readers how to immediately implement the concepts discussed within to help solve real-world problems.